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Milstein’s type schemes for fractional SDEs
16 references·2 citing·44 second hop
Milstein’s type schemes for fractional SDEs (2009)Milstein’s type schemes for fractional SD…Central and non-central limit theorems for weighted power variations of fractional Brownian motion (2010)Central and non-central limit…The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion (2008)The rate of convergence for E…Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation (2008)Differential Equations Driven…Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2007)Exact Rate of Convergence of …Power variation of some integral fractional processes (2006)Power variation of some integ…m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index (2004)m-order integrals and general…Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales (2003)Approximation at First and Se…Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Stochastic analysis, rough pa…Differential equations driven by fractional Brownian motion (2002)Differential equations driven…Integration with respect to fractal functions and stochastic calculus. I (1998)Integration with respect to f…Differential equations driven by rough signals (1998)Differential equations driven…Stochastic analysis of fractional brownian motions (1995)Stochastic analysis of fracti…Forward, backward and symmetric stochastic integration (1993)Forward, backward and symmetr…Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's (1991)Wong-Zakai Corrections, Rando…Resolution trajectorielle et analyse numerique des equations differentielles stochastiques (1983)Resolution trajectorielle et …On Quadratic Variation of Processes with Gaussian Increments (1975)On Quadratic Variation of Pro…Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method (2013)Estimation of the Hurst param…Discretizing the fractional Lévy area (2009)Discretizing the fractional L…Fractional Brownian Motions, Fractional Noises and Applications (1968)Stochastic Analysis of the Fractional Brownian Motion (1999)Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion (2008)Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion (2008)Fractional stochastic differential equations with applications to finance (2012)On the Convergence of Ordinary Integrals to Stochastic Integrals (1965)Weak Limit Theorems for Stochastic Integrals and Stochastic Differential Equations (1991)Weak convergence of stochastic integrals and differential equations (1996)An Introduction to Rough Paths (2003)Stochastic Integration and Differential Equations : A New Approach (2014)Stochastic Differential Equations and Diffusion Processes (1983)Continuous Martingales and Brownian Motion (1999)Stochastic integration with respect to fractional brownian motion (2003)Brownian Motion and Stochastic Calculus (2007)Differential Equations Driven by Rough Paths (2007)Calcul Stochastique et Problèmes de Martingales (1979)Continuous Martingales and Brownian Motion (1991)Stochastic integration with respect to the fractional Brownian motion (2003)Analysis of the Rosenblatt process (2008)Multiple Wiener Integral (1951)Integration questions related to fractional Brownian motion (2000)Stochastic Calculus with Respect to Gaussian Processes (2001)Stochastic Flows and Stochastic Differential Equations (1998)Integrability and tail estimates for Gaussian rough differential equations (2013)Geometric versus non-geometric rough paths (2015)Numerical solution of stochastic differential equations (2016)Differential equations driven by rough paths with jumps (2018)Itô′s formula with respect to fractional Brownian motion and its application (1996)Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 12 (2000)Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter H∈(0,12) (2005)Stochastic Integration and Differential Equations (2005)Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models (2002)Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics (2004)Power and Bipower Variation with Stochastic Volatility and Jumps (2004)Power variation for Gaussian processes with stationary increments (2008)Multipower variation for Brownian semistationary processes (2011)Convergence of integrated processes of arbitrary Hermite rank (1979)Gaussian Limits for Vector-valued Multiple Stochastic Integrals (2004)The Malliavin Calculus and Related Topics (2006)Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion (2008)The optimal fourth moment theorem (2015)Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017)Controlling rough paths (2004)Multidimensional Stochastic Processes as Rough Paths (2010)
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References

  • 1998Differential equations driven by rough signals1,077 cited
  • 1998Integration with respect to fractal functions and stochastic calculus. I589 cited
  • 2002Differential equations driven by fractional Brownian motion408 cited
  • 1993Forward, backward and symmetric stochastic integration318 cited
  • 2002Stochastic analysis, rough path analysis and fractional Brownian motions317 cited
  • 1995Stochastic analysis of fractional brownian motions207 cited
  • 2008Differential Equations Driven by Rough Paths: An Approach via Discrete Approximation156 cited
  • 2010Central and non-central limit theorems for weighted power variations of fractional Brownian motion127 cited
  • 2006Power variation of some integral fractional processes110 cited
  • 1991Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's105 cited
  • 2004m-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index101 cited
  • 2007Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion100 cited
  • 2008The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion81 cited
  • 1975On Quadratic Variation of Processes with Gaussian Increments

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58 cited
  • 2003Approximation at First and Second Order of $m$-order Integrals of the Fractional Brownian Motion and of Certain Semimartingales50 cited
  • 1983Resolution trajectorielle et analyse numerique des equations differentielles stochastiques42 cited
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